Multiple Time Scale Dynamical Systems

Author : Kristine Dianna O'Laughlin
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.6/5 (721 download)

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Download or read book Integration of Multiple Time-scales in Psychology written by Kristine Dianna O'Laughlin and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientists have long pondered the mechanisms behind how and why systems change and evolve over time. In psychology, change is centered at the level of the individual, and understanding how the individual changes in the short-term (i.e., intraindividual variability), and evolves in the long-term (i.e., intraindividual change), is important to understanding development. The merger of these two concepts is realized when data are collected across multiple time-scales, and current technological advances (e.g., electronically-activated recording devices) have not only made the collection of these types of data a possibility, but have also allowed us to grow even closer to being able to capture life as it unfolds in real time. However, with such rich data becoming more accessible, this poses unique challenges for study design and analysis of multiple time-scale data. In psychology, a common method of analysis of multiple time-scale data has been multilevel modeling techniques in which the process that fluctuates more rapidly is conceptualized to be nested within the slower-moving process. A competing data analytic approach which has been growing in popularity is the use of dynamical systems, which utilize differential equations to relate variables to their derivatives in order to examine change in continuous time. In psychology, we are usually concerned with first and second derivatives corresponding to velocity and acceleration, respectively. In addition to these considerations for analysis of multiple time-scale data, the chosen sampling interval and sampling strategy have implications for what types of research questions can be answered about the dynamics within a system, and traditional longitudinal panel designs may be ill-equipped to answer some of our most complex research questions. Therefore, the purpose of this dissertation is to (a) compare multilevel modeling and dynamical systems approaches for analyzing multiple time-scale data; (b) evaluate recovery of dynamic parameters under different design and sampling conditions; and (c) illustrate the above issues through analysis of empirical data. The first chapter provides historical background and explicates goals of longitudinal research, emphasizing the importance of understanding both intraindividual variability and intraindividual change. The second chapter discusses the current univariate and multivariate approaches to analysis of data collected at multiple time-scales. Moreover, in this chapter, data were generated from multilevel and dynamical systems models, and models were compared in their abilities to recover the driving mechanism of change. Findings from this study suggest that the multilevel model and a differential equation model of acceleration were most successful at recovering the driving process. The differential equation model of velocity, however, was poor at identifying the driving process and recovering the relative contribution of each process. The third chapter discusses issues related to various sampling schemes and how they relate to collection of multiple time-scale data. In this chapter, data from Chapter 2 were sampled so that the slower process was measured less frequently than the faster process. Models were then fit to these data where the measured time-scales differed between the processes. Findings indicate that the multilevel model approach required fitting a simpler model to accommodate this sampling, while the dynamical systems models differed in their abilities to recover dynamic parameters. While the differential equation model of acceleration provided a fairly good recovery of the driving process, the model of velocity tended to suggest bidirectional effects when only one process drove changes in the true model. In the fourth chapter, an analysis of empirical data was conducted to illustrate issues related to analysis of multiple time-scale data. This study suggests that relations between physical activity and mood differ depending on whether the modeled outcome is level, velocity, or acceleration. The fifth and final chapter provides a general discussion of findings from Chapters 2-4, discusses limitations to this study, and offers future directions and recommendations for researchers interested in collecting and analyzing data derived from multiple time-scales.